Certainly! Let's tackle each question step by step.
### Question 1:
What is the result when the quotient of 4x^6 and -2x^2 is raised to the third power?
First, find the quotient of [tex]\(4x^6\)[/tex] and [tex]\(-2x^2\)[/tex]:
[tex]\[
\frac{4x^6}{-2x^2} = -2x^4
\][/tex]
Now, we need to raise this result to the third power:
[tex]\[
(-2x^4)^3
\][/tex]
Using exponential rules:
[tex]\[
(-2)^3 \cdot (x^4)^3
= -8 \cdot x^{12}
\][/tex]
So, the answer is:
[tex]\[
\boxed{-8x^{12}}
\][/tex]
### Question 2:
What is the 10th term in the pattern 1, 8, 27, 64 ...?
This sequence is a series of cubes:
[tex]\[
1^3, 2^3, 3^3, 4^3, \ldots
\][/tex]
Therefore, the 10th term is:
[tex]\[
10^3 = 1000
\][/tex]
So, the 10th term is:
[tex]\[
\boxed{1000}
\][/tex]
### Question 3:
What algebraic expression represents the phrase "Four times a number (x) more than twelve"?
The phrase translates directly into the algebraic expression as:
[tex]\[
4x + 12
\][/tex]
So, the expression is:
[tex]\[
\boxed{4x + 12}
\][/tex]
These answers fully address each part of the question.
